1. Field of the Invention
The present invention relates to an air fuel ratio control apparatus for an internal combustion engine.
2. Description of the Related Art
In general, a catalytic converter (hereinafter referred to simply as a “catalyst”) with a three-way catalyst received therein for purifying harmful components HC, CO, NOx in an exhaust gas at the same time is installed in an exhaust passage of an internal combustion engine. Since such a kind of catalyst has a high purification rate for any of HC, CO and NOx in the vicinity of a stoichiometric air fuel ratio, an oxygen sensor is generally arranged at an upstream side of the catalyst so that an air fuel ratio of an air fuel mixture is controlled so as to make the air fuel ratio upstream of the catalyst become in the vicinity of the stoichiometric air fuel ratio.
In addition, the upstream oxygen sensor at the upstream side of the catalyst is arranged at a location of an exhaust system as close to combustion chambers as possible (i.e., a merged or collected portion of an exhaust manifold located upstream of the catalyst), and it is subjected to high exhaust temperatures and a variety of kinds of toxic substances, so the output characteristic of the oxygen sensor is caused to vary to a great extent.
Accordingly, a duel oxygen sensor system has been proposed in which in order to compensate for the characteristic variation of the upstream oxygen sensor, a downstream oxygen sensor is arranged at a location downstream of the catalyst, so that second air fuel ratio feedback control according to the downstream oxygen sensor is performed in addition to first air fuel ratio feedback control according to the upstream oxygen sensor (see, for example, a first patent document: Japanese patent application laid-open No. S63-1 95351 and a second patent document: Japanese patent application laid-open No. H6-42387).
The downstream oxygen sensor is low in response speed in comparison with the upstream oxygen sensor but has the following merits. That is, at the downstream side of the catalyst, the temperature of the exhaust gas is low, and hence the influence of heat is small, and in addition, various toxic substances are trapped by the catalyst, so the poisoning of the oxygen sensor is small, and the variation of the output characteristic of the oxygen sensor is small. Further, at the downstream side of the catalyst, the exhaust gas is mixed to a satisfactory extent, so the state of purification of the catalyst located at an upstream side can be detected in a stable manner.
Thus, in the duel oxygen sensor system, by correcting the upstream air fuel ratio and maintaining the output value of the downstream oxygen sensor to a target value, the variation of the output characteristic of the upstream oxygen sensor is compensated for, and the state of purification of the catalyst is adequately maintained.
In addition, for the purpose of absorbing a temporary variation of the upstream air fuel ratio from the stoichiometric air fuel ratio, the oxygen storage capability is added to the catalyst, whereby the catalyst takes in and accumulates oxygen in the exhaust gas when the air fuel ratio thereof is leaner than the stoichiometric air fuel ratio, whereas the catalyst releases the oxygen accumulated therein when the air fuel ratio is richer than the stoichiometric air fuel ratio.
In this manner, the catalyst has an annealing operation (or delayed averaging operation), and hence the variation of the air fuel ratio at the upstream side of the catalyst is processed in the catalyst in a delayed manner to provide an air fuel ratio at the downstream side of the catalyst. In addition, an upper limit value of the amount of oxygen storage is decided by the amount of a material with an oxygen storage capability which is added upon production of the catalyst.
Accordingly, when the amount of oxygen storage is saturated to the upper limit value or lower limit value (=0), the delay operation to absorb the variation of the upstream air fuel ratio no longer exists, so the air fuel ratio in the catalyst comes off from the stoichiometric air fuel ratio, and the purification ability of the catalyst reduces. At this time, the air fuel ratio downstream of the catalyst deviates greatly from the stoichiometric air fuel ratio, so it is possible to detect that the amount of oxygen storage in the catalyst has reached the upper limit value or lower limit value (=0).
When the amount of oxygen storage of the catalyst becomes a value between the upper limit value and the lower limit value, generating a delay operation of the catalyst, the purification rate of any of HC, CO and NOx in the exhaust gas becomes high, and in particular, the purification rate becomes the highest when the amount of oxygen storage of the catalyst is in an intermediate level between the upper limit value and the lower limit value. In addition, the amount of oxygen storage of the catalyst can be detected due to a minute change in the vicinity of the stoichiometric air fuel ratio of the downstream air fuel ratio. As a result, by controlling the output value of the downstream oxygen sensor to a target value, it is possible to control the amount of oxygen storage to an appropriate amount thereby to maintain the purification rate of the catalyst high.
Thus, to keep exhaust gas purification performance in an adequate manner, the stability of the feedback control using the downstream oxygen sensor (having a delay operation for the catalyst to be controlled) is important.
In addition, in a so-called PID feedback control using proportional calculation, integral calculation and differential calculation, the stability and response of the feedback control change in accordance with the magnitudes of a proportional gain Kp, an integral gain Ki and a differential gain Kd. That is, if the individual gains are set to be small, the stability is improved but the response is deteriorated. On the contrary, if the individual gains are set to be great, the stability is deteriorated but the response is improved.
A control quantity for the PID feedback control is represented, as shown by the following expression (1), by using a deviation err(t) between an actual value and a target value and the individual gains Kp, Ki and Kd.control quantity=Kp×err(t)+Ki×∫0terr(t)dt+Kd×derr(t)/dt   (1)
In a control object having a saturation state for the upper limit amount or the lower limit amount in which there exists no response delay, as in the oxygen storage operation of the catalyst, the stability of a control system decreases in accordance with the increasing set value for the proportional gain Kp, and finally it reaches a state in which a sustained oscillation continues. Here, note that even if the proportional gain Kp is set to be further greater, the control system becomes stable in the state of the sustained oscillation, and hence there is no change in the stability of the control system.
FIG. 19 is a timing chart illustrating the change over time of an output value of a general downstream oxygen sensor, wherein the waveforms of mutually different proportional gains Kp are shown respectively.
As shown in FIG. 19, the proportional gain Kp, the integral gain Ki and the differential gain Kd, which can provide good control performance, are set with a proportional gain Kpc and a sustained oscillation period Tc, at the time when the set value of the proportional gain Kp is gradually increased, being made as references. Such a gain setting method is called a limit sensitivity method in which a setting rule is applied as shown in the following expressions (2).Kp=A×Kpc Ki=B×Kpc/Tc Kd=C×Kpc×Tc   (2)
In the above expressions (2), individual constants A, B, C are values that are adjusted in accordance with the kinds of delays of the object to be controlled such as, for example, a dead time delay, a primary delay, a secondary delay, etc, or in accordance with the design of a transient response.
In the feedback control using the downstream oxygen sensor, a delay in the oxygen storage operation of the catalyst is very large and predominant in comparison with other delays, and the limit of stability depends on the oxygen storage operation. This is because the delay in the oxygen storage operation of the catalyst is designed to be sufficiently great so as to absorb the variation of the air fuel ratio due to other delays such as a delay of the oxygen sensor, a delay in movement of the exhaust gas, etc.
In addition, the change rate of the amount of oxygen storage of the catalyst is proportional to the amount of change of the air fuel ratio at the upstream side of the catalyst from the stoichiometric air fuel ratio and the flow rate of exhaust gas qa.
FIG. 20 through FIG. 22 are timing charts illustrating the output value of the downstream oxygen sensor, an upstream target air fuel ratio, and the change over time of the amount of oxygen storage of the catalyst in association with one another, wherein FIG. 20 shows a case when the flow rate of exhaust gas qa is in a small level, FIG. 21 shows a case when the flow rate of exhaust gas qa is in an intermediate level, and FIG. 22 shows a case when the flow rate of exhaust gas qa is in a large level.
Also, in FIG. 20 through FIG. 22, the behaviors of the stability limit (sustained oscillation period Tc) are illustrated when the flow rate of exhaust gas qa changes from the small level to the large level through the intermediate level (i.e., small→intermediate→large). The amount of change of the air fuel ratio at the upstream side of the catalyst is decided in accordance with the magnitude of the proportional gain, so the proportional gain Kpc of the stability limit is not caused to change by the flow rate of exhaust gas qa. On the other hand, the change rate of the amount of oxygen storage is proportional to the flow rate of exhaust gas qa, so the sustained oscillation period Tc decreases in accordance with the increasing flow rate of exhaust gas qa, and the following expressions (3) hold.Kpc=constantTc∝1/qa   (3)
Accordingly, complying with the setting rule of the limit sensitivity method according to the above-mentioned expressions (2), an optimal PID gain becomes as shown by the following expressions (4).Kp=definite valueKi∝qaKd∝1/qa   (4)
In addition, in the past, there has been known a method of changing the control gain of feedback control using a downstream oxygen sensor in accordance with the flow rate of an exhaust gas (see, for example, a third patent document: Japanese patent application laid-open No. S63-208639, a fourth patent document: Japanese patent application laid-open No. H10-26043, and a fifth patent document: Japanese patent application laid-open No. 2002-227689).
In the third and fourth patent documents, the integral gain (the amount of update) of integral calculation is set so as to proportional to the flow rate of the, exhaust gas, so it is possible to achieve a highly stable control behavior that suits the delay of the oxygen storage operation of the catalyst.
Also, in the fifth patent document, it is designed such that the proportional gain and the integral gain are set in accordance with the exhaust gas flow rate.
In the conventional air fuel ratio control apparatuses for an internal combustion engine, for example in case of the third and fourth patent documents, feedback control is constituted only by integral calculation, so the response of the feedback control is poor in comparison with the case in which integral calculation and proportional calculation are used, thus giving rise to a problem that it is difficult to converge the state of purification of the catalyst deteriorated by external disturbances, etc., into a target value in a swift manner.
In addition, there has also been another problem that even if the integral gain can be set appropriately, the stability of the control system might be deteriorated depending upon the set value of the proportional gain Kp, and hence such a setting does not contribute to a satisfactory solution.
Moreover, in the fifth patent document, the proportional gain and the integral gain are set to be in inverse proportion to the exhaust gas flow rate, so there arises a further problem as stated below. That is, it is difficult to achieve a control behavior that suits the behavior of the amount of oxygen storage of the catalyst, and in addition, a more complicated construction is required so as to prevent hunting by changing a guard value of the control quantity in proportion to the exhaust gas flow rate, or by providing an intermediate target value.
Thus, with the conventional air fuel ratio control apparatuses for an internal combustion engine, in the so-called PID feedback control using proportional calculation, integral calculation and differential calculation, it is impossible to set a control gain with good stability and controllability appropriate for the delay in the oxygen storage operation of the catalyst, so there is a problem that the state of purification of the catalyst can not be kept adequately with good controllability.